## Section 5.2 - Mean Value Theorem

**Essential Question(s):**

What is the Mean Value Theorem and its applications?

**Follow**__these three steps__to complete this "flip" lesson.**STEP 1: Preparation**

__Title__your spiral with the heading above and

__copy__the essential question(s).

**STEP 2: Vocabulary & Examples**

__Copy__and

__define__the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed.

__Review__the following examples and

__copy__what is necessary for you. Use the guiding questions for your Cornell notes.

__Mean Value Theorem__

- What is the Mean Value Theorem? (pg 202 paragraphs and diagrams)
- Exploring the Mean Value Theorem. (Ex 1 and Ex 2 pg 202-203)
- How do you apply the Mean Value Theorem? (Ex 3 pg 204)

__Physical Interpretation__

- What does the Mean Value Theorem mean? (pg 204)
*Read Example 4 and take notes as needed. (pg 204)*

__Increasing and Decreasing Functions__

- What is the definition of increasing and decreasing functions? (pg 204)
- What are monotonic functions? (sidebar pg 204)
- How does the Mean Value Theorem help with increasing and decreasing functions? (pg 204-205)
- How do you determine where a graph rises or falls? (Ex 5 and 6 pg 205; sidebar pg 205)

__Other Consequences__

- How does the Mean Value Theorem help with constant functions? (pg 205)
- How does the Mean Value Theorem help with functions with the same derivative? (pg 205)
- How do you apply corollary 3? (Ex 7 pg 206)
- What is an antiderivative? (pg 206 - 207)
- How do you find velocity and position? (Ex 8 pg 207)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 202 - 207.
- Make sure to read the paragraphs between the examples and sidebar snippets.